The aim of this research was to evaluate the clumped model for estimating latent heat flux (LE) and actual evapotranspiration (ETa) over a non-water-stressed olive orchard. Additionally, submodels to compute the net radiation Rn, soil heat flux G, and canopy resistance were also included. For this objective, a database was used from an experimental unit inside a commercial superintensive drip-irrigated olive orchard located in the Pencahue Valley, Maule Region, Chile (35°23′S, 71°44′W; 96 m above sea level) during the 2009/10 and 2010/11 growing seasons. The evaluation was carried out using measurements of LE obtained from an eddy covariance (EC) system. In addition, estimated values of Rn, G, and were compared with ground-truth measurements from a four-way net radiometer, soil heat flux plates with soil thermocouples, and a portable porometer, respectively. Results indicated that the clumped model underestimated LE and ETa with errors of 11.0% and 3.0%, respectively. Values of the root-mean-square error (RMSE), mean bias error (MBE), and index of agreement dr for LE were 35 W m−2, −1.0 W m−2, and 0.96, while those for ETa were 0.48 mm day−1, 0.04 mm day−1, and 0.64, respectively. The submodels computed Rn and G with errors less than 6% and RMSE values less than 65 W m−2, while the Jarvis-type model predicted with RMSE = 41 s m−1 and MBE = 7.0 s m−1. Finally, a sensitivity analysis indicated that the ETa estimated by the clumped model was significantly affected by variations of ±30% in the values of the LAI and the minimum stomatal resistance rstmin.
The water availability for irrigation has been reduced in the recent years due to frequent drought and competition between agriculture, industrial, and urban areas (Molden et al. 2010; Calzadilla et al. 2010; Hoekstra et al. 2012). The Mediterranean oliviculture areas, such as Chile, have been significantly affected by the changes in precipitation at local scale (Meza et al. 2012). Water scarcity has become into the main limitation to maintain the olive oil production. Thus, the estimation of water requirements plays an important role in establishing irrigation managements of olive orchards under water scarcity scenarios. The water consumption is estimated through the computation of the actual evapotranspiration (ETa), which is a function of the reference evapotranspiration (ETo) and crop coefficients Kc (Allen et al. 1998). The main limitation of this approach is the selection of the right value of Kc, which may be markedly influenced by tree vigor, the training system (expressed in LAI and fractional vegetation cover fc values) and nonlinear interactions of the soil, the cultivar and the climate conditions (López-Olivari et al. 2016; Martínez-Cob and Faci 2010). Additionally, Kc values can be affected by the partitioning of net radiation Rn into latent (LE), sensible H, and soil G heat fluxes. For a drip-irrigated olive orchard, Testi et al. (2004) showed that there was more energy distributed to evapotranspiration (LE) than to heating air (H) as the leaf area increased from 0.01 to 1.0 m2 m−2. Additionally, Ortega-Farias et al. (2016) indicated that in a drip-irrigated olive orchard (fc = 0.31 and LAI = 1.32 m2 m−2), the H produced at the soil surface between rows was the main component of the orchard energy balance that affected the partitioning of ETa into transpiration T and soil evaporation E. Thus, the direct estimation of ETa over heterogeneous (or discontinuous) canopies of such orchards is very complex because water requirements are significantly affected by the partitioning of energy balance over the soil surface and the tree canopy.
For discontinuous canopies, incomplete soil cover leads to a differentiation of LE from soil in two sources: 1) soil under the canopy and 2) the bare soil between rows. Source 1 generates high LE and low H because there is high water content in the soil surface from the wetted area below the drippers, while source 2 yields low LE and high H because the water content in the soil surface is low, even close to the wilting point. Under these conditions, several researchers have suggested using clumped models to directly estimate ETa over discontinuous canopies such as fruit orchards and vineyards (Poblete-Echeverría and Ortega-Farias 2009; Were et al. 2008; Zhou et al. 2006). The effectiveness of estimating ETa from discontinuous clumped canopies has been reported in the literature (Domingo et al. 1999; Poblete-Echeverría and Ortega-Farias 2009; Were et al. 2008) considering the modifications proposed by Brenner and Incoll (1997) to the sparse-crop model of Shuttleworth and Wallace (1985). These modifications generated the clumped model, an approach that uses a mixture between the Shuttleworth–Wallace model and the energy distribution proposed by Dolman (1993), who suggested weighing the partitioning by the fractional cover from the plant and bare soil. The clumped model considers three sources from where LE is transferred to the atmosphere: the canopy, the soil under canopy, and the soil between rows. Then, ETa is obtained by the sum of Penman–Monteith equations that estimate LE from each source, weighed by their fractional covers and a set of coefficients that represent the combination of aerodynamic resistances (Poblete-Echeverría and Ortega-Farias 2009). Unlike the Shuttleworth–Wallace model, which assumes that vegetation is uniformly distributed over a surface, the clumped model takes into account the clumping of the vegetation. This consideration would explain the changes in the energy absorbed by the plant canopy and the substrate below it (Brenner and Incoll 1997). In summary, this model differentiates LE sources into vegetative and nonvegetative components.
The clumped model has been applied in several heterogeneous canopies with an RMSE for ETa ranging from 0.13 to 1.85 mm day−1. For discontinuous canopy (fc = 34%, LAI is between 1.71 and 3.4 m2 m−2), Brenner and Incoll (1997) indicated that the clumped model underestimated T with an error of 5%. For bush vegetation in Spain (fc = 17%, LAI = 0.81 m2 m−2), Were et al. (2008) found that the clumped model estimated ETa with an RMSE of 0.13 mm day−1. For a discontinuous vegetated stand (Anthyllis cytisoides L.) (fc = 40%, LAI between 0.66 and 1.44 m2 m−2), Villagarcía et al. (2010) reported RMSE values ranging from 0.21 to 1.85 mm day−1. For a furrow-irrigated vineyard (fc = 35% and LAI = 0.2 m2 m−2) in the arid desert region of northwest China, Zhang et al. (2008) observed that the clumped model underestimated LE by approximately 1% with a MAE of 32 W m−2. Finally, for a drip-irrigated Merlot vineyard (fc = 30% and LAI between 0.6 and 1.25 m2 m−2), Poblete-Echeverría and Ortega-Farias (2009) estimated the LE and ETa with RMSE values of 33 W m−2 and 0.32 mm day−1, respectively.
To our knowledge, there is little information about the evaluation of LE and ETa over hedge-pruned olive orchards trained on a superintensive system. Thus, the objective of this research was to parameterize the clumped model for estimating LE and ETa over a commercial superintensive drip-irrigated olive orchard (Olea europaea L. cv. Arbequina) under non-water-stress conditions. Additionally, this study includes a parameterization of submodels for estimating Rn, G, and .
2. Materials and method
a. Study site
A superintensive drip-irrigated olive orchard (cv. Arbequina) located in the Pencahue Valley, Maule Region, Chile (35°23′S, 71°44′W; 96 m above sea level) was used to evaluate the clumped model during the 2009/10 and 2010/11 growing seasons. The experimental unit presented a clay loam texture soil texture and was classified as the Quepo series (Vertisol; fine, Thermic Xeric Apiaquerts). The trees were trained on a hedgerow system with a row spacing of 5.0 m × 1.5 m and irrigated using two drippers per tree at a 2.0 L h−1 flow rate.
b. Field measurements
1) Plant and soil monitoring
For irrigation management, the midday stem water potential was measured at solar noon using a pressure chamber (PMS 1000, PMS Instrument Co., Corvallis, OR) during the two growing seasons (from flowering to harvest). A shoot (two per tree, one tree per replicate) with five or six pairs of leaves was encased in a plastic bag and wrapped in aluminum foil at least 2 h before measurement (Gómez-del-Campo 2013; Pierantozzi et al. 2013; Tognetti et al. 2007). Moreover, soil water content Θ at the 0–60-cm depth was measured using a portable time domain reflectometry unit (TRASE, Soil Moisture Corp., Santa Barbara, CA) with 20 pairs of rods inserted within and between the wet bulbs. Additionally, stomatal resistance rst was measured using a portable porometer (PMR-5, PP Systems, Amesbury, MA). Finally, the LAI was measured weekly using a plant canopy analyzer (LAI-2000, LI-COR, Lincoln, NE), which was calibrated defoliating six trees for the two periods, where the leaves of each tree were photographed, and then the total leaf area per tree was measured using a digital image analysis. The calibrated equation was y = 0.293x + 0.658 (r2 = 0.91), where y corresponds to the measured LAI from the defoliated trees and x is the uncalibrated LAI from the LAI-2000 measurements.
2) Surface energy balance data
The sensor descriptions for measuring meteorological variables and orchard energy balance components recorded by dataloggers (CR1000–CR5000, Campbell Scientific Inc., Logan, UT) are indicated in Table 1. The fast response and open-path infrared gas analyzer and the three-dimensional sonic anemometer were installed with a lateral separation of approximately 0.1 m for the EC system. The raw data (10 Hz) was postprocessed using the EdiRe software (University of Edinburgh, United Kingdom), which included the corrections of coordinate rotation (Wilczak et al. 2001), sonic temperature (Schotanus et al. 1983), and density effect (Webb et al. 1980). Surface energy balance data with unusual instrumental behavior, power failure and rain events were not used to validate the model. Moreover, ETa was calculated as the sum of LE between 0800 and 2000 UTC, in order to take into account only the mixing boundary layer (strong turbulence). The quality control of data was done through the computation of the energy balance closure using the energy balance ratio (EBR) as described below (Wilson et al. 2002):
where Rn is the net radiation (W m−2), Gavg is the average soil heat flux (W m−2), and Hec and LEec are the sensible and latent heat fluxes (W m−2) computed after raw data postprocessing, respectively. To reduce the uncertainty associated with errors in the LE measurements, those days that presented an EBR with acceptable closure according to literature (0.8 < EBR < 1.2) were used in the analysis, otherwise they were discarded (Twine et al. 2000; Wilson et al. 2002; Liu et al. 2011; Ortega-Farias and López-Olivari 2012). Furthermore, the values of LEec for the selected days were recalculated using the Bowen ratio β as follows (Twine et al. 2000; Martínez-Cob and Faci 2010):
After applying the data quality control, 47 days were available to validate the clumped model.
c. Model description
The actual evapotranspiration (ETa; mm day−1) of the superintensive drip-irrigated olive orchard was estimated using the following expression:
where LEci is the latent heat flux estimated by the clumped model (W m−2) at 30-min intervals, λ is the latent heat of vaporization (MJ kg−1), is the density of water (kg m−3), N is the number of measurements during the day. The 1800 number is a time conversion of s (30 min)−1.
The clumped model computes LEc as the sum of olive transpiration T, evaporation from soil under the canopy Es, and evaporation from soil between rows Ebs weighted by the fc (Brenner and Incoll 1997):
where PMc, PMs, and PMbs are Penman–Monteith type combination equations for estimating the canopy transpiration, evaporation from soil under canopy, and bare soil between rows (all in W m−2), respectively; Cc is the canopy resistance coefficient; Cs is the soil resistance coefficient under plant; and Cbs is the soil resistance coefficient between rows (all dimensionless). These coefficients were calculated by the following equations:
where A, As, and Ac (all in W m−2) correspond to the total energy available from the olive orchard and soil under tree canopy and olive canopy, respectively; ρ is the air density (kg m−3); Δ is the slope of the vapor pressure versus temperature curve (kPa °C−1); γ is the psychrometric constant (kPa °C−1); Cp is the specific heat capacity of the air at constant pressure (J kg−1 K−1); D is the vapor pressure deficit of the air (kPa) at the reference height zr; is the aerodynamic resistance (s m−1) of the olive from the leaf surface to the mean surface flow height zm; is the aerodynamic resistance (s m−1) between zm and zr; is the aerodynamic resistance (s m−1) between the bare soil surface between rows at zm; is the aerodynamic resistance (s m−1) between the soil under olive canopy at zm; is the canopy resistance (s m−1); is the soil surface resistance (s m−1) under olive canopy; and is the soil surface resistance (s m−1) between rows. The values of Rc, Rs, Ra, and Rbs are estimated as follows:
1) Available energy using meteorological data
The values of A, Ac, and As were computed using the following expressions:
where Rne is the estimated net radiation over the olive orchard (W m−2), Ge is the estimated soil heat flux (W m−2), Rns is the net radiation absorbed by the soil under canopy (W m−2), LAI is the leaf area index (m2 m−2), and C is the extinction coefficient of the canopy for net radiation (dimensionless). The Rne was computed as follows (Chávez et al. 2005; Ezzahar et al. 2007):
where α is the surface albedo (dimensionless), Rsi is the incoming shortwave radiation (W m−2), is the atmospheric emissivity (dimensionless), σ is the Stefan–Boltzmann constant (W m−2 K−4), is the emissivity of the surface (dimensionless), Ta is the air temperature (K), Ts is the surface temperature (K), Tsoil is the soil temperature (K), and Tc is the canopy temperature (K). The Tsoil was obtained from a soil thermocouple buried at 8-cm depth; meanwhile, Tc was derived from the inverted longwave radiation measured by a four-way net radiometer (CNR1, Kipp and Zonen, Delft, The Netherlands). Also, and are the emissivity of the canopy and soil, respectively. Values of were computed from air temperature and vapor pressure as (Brutsaert 1982):
where ew is the air vapor pressure (kPa) and ϕ is the calibration coefficient (dimensionless). To estimate Ge, a regression analysis between Rn and Gavg was performed using an independent dataset (50 days). In this case, G was estimated as follows (coefficient of determination r2 = 0.78):
2) Aerodynamic resistances
Using the Shuttleworth and Gurney (1990) approach, values of aerodynamic resistance were estimated by the following expressions:
where rb is the mean boundary layer resistance of leaf per unit surface area of vegetation (s m−1), η is the attenuation coefficient for wind speed (dimensionless), n is the eddy diffusivity decay coefficient (dimensionless), w is the average leaf width (m), a is a constant (dimensionless), uh is the wind speed (m s−1) at the top of the canopy average height, d is the displacement height (m), h is the height of the olive canopy (m), k is the von Kármán’s constant (dimensionless), zo is the roughness length (m), is the friction velocity (m s−1), ur is the wind speed at zr (m s−1), cd is the drag coefficient (dimensionless), and is the roughness length of the bare soil (m).
The values of and were estimated by the following expressions:
where dp is the zero-plane displacement height (m) (taken as 0.63h), Zo is the zero roughness length of the surface (m) (taken as 0.13h), and Kh is the diffusivity at the top of the canopy (m2 s−1). The values of aerodynamic resistance between the bare soil surface and zm were calculated assuming a linear variation between and with fc changing from 0 to 1 (Brenner and Incoll 1997; Villagarcía et al. 2007):
where is the aerodynamic resistance (s m−1) of bare soil completely unaffected by vegetation and um is the wind speed (m s−1) at zm.
3) Canopy resistance
The canopy resistance was estimated considering the Jarvis approach, according the equations used by Zhao et al. (2015):
where rstmin is the minimal stomatal resistance (s m−1); meanwhile F1, F2, F3, and F4 (all dimensionless) indicate the effect of the photosynthetically active radiation, vapor pressure deficit of the atmosphere, air temperature, and soil moisture stress, respectively. Values of F1, F2, F3, and F4 were estimated as follows (Noilhan and Planton 1989):
where rstmax is the maximum stomatal resistance (s m−1), Rsl corresponds to the threshold radiation (W m−2) value above the stomata openness, and Ta is the air temperature (K). Values of , , and are actual, maximum, and minimum soil water contents (m3 m−3), respectively.
The observed values of were computed according to Lafleur and Rouse (1990):
For the clumped model, constant values used in this study are indicated in the Table 2.
e. Model performance
The performance of the clumped model was evaluated using the ratio of observed to estimated values roe, the root-mean-square error (RMSE), mean bias error (MBE), and index of agreement dr. These statistical parameters are described as follows:
where N is the total number of observations; Ei and Oi are the estimated and observed values, respectively; and is the mean of the observed values. Finally, a sensitivity analysis of the resistances ( and ), LAI and constant variables (C, d, dp, n, zo, , and Zo, rstmin, and rstmax) was conducted to assess their effects on the performance of the clumped model for estimating ETa. To do this, the percent deviation of the mean ETa was calculated when the LAI value, constant variables and resistances individually varied by ±30%.
3. Results and discussion
The climatic conditions over the olive orchard were hot and dry during the two growing seasons. Table 3 indicates that mean values of Ta were between 17.7° and 21.1°C while those of D ranged between 1.0 and 4.0 kPa. Furthermore, the daily maximum Rn ranged between 667 and 764 W m−2 for both seasons. In the case of u, the average was approximately 1.5 m s−1, with a maximum value of 4.7 m s−1.
For the 2009/10 growing season, the average θ at 20- and 60-cm depth under the canopy were 0.09 and 0.23 m3 m−3, while those for the 2010/11 growing season were 0.11 and 0.18 m3 m−3, respectively. Meanwhile, the θ at 20-cm depth between rows for both growing seasons ranged 0.14–0.11 m3 m−3, respectively. Under these soil moisture conditions, ranged between −1.43 and −1.96 MPa indicating that the olive trees were under null to mild water stress (Ahumada-Orellana et al. 2017). Additionally, the average values of fc, LAI, and rst were between 29% and 30%, between 1.16 and 1.65 m2 m−2, and between 181 and 283 s m−1, respectively.
The obtained ratio of turbulent fluxes (Hec + LEec) to available energy (Rn − G) was different from one (EBR = 0.87) indicating that the EC measurements presented a lack of energy closure equal to 13% (Fig. 1). For a young drip-irrigated orchard (fc = between 1% and 25% and LAI = between 0.1 and 1.0 m2 m−2), Testi et al. (2004) reported an energy closure ranging between 85% and 95%, while for a flood-irrigated olive orchard, Williams et al. (2004) found a lack of energy closure of 26%. Ezzahar et al. (2007) reached an energy closure of 95% over a flood-irrigated olive orchard (fc = 55%). Er-Raki et al. (2008) showed a lack of energy balance closure between 8% and 10% over a flood-irrigated olive orchard (fc = between 15% and 20% and LAI = 3.0 m2 m−2). Cammalleri et al. (2013) obtained an energy closure between 90% and 92% in a drip-irrigated olive orchard (fc = 35% and LAI between 1.1 and 2.4 m2 m−2). Finally, Martínez-Cob and Faci (2010) obtained a lack of energy closure equal to 26% in a drip-irrigated hedge-pruned olive orchard (fc = 34%). Therefore, the literature shows a general lack of energy balance closure between 5% and 20% even under ideal fetch conditions (Twine et al. 2000; Wilson et al. 2002). Based on this problem, many sources of the lack of energy balance closure have been proposed, such as 1) errors in measurements, 2) incorrect accounting for the storage of energy in the soil and canopy, or 3) advective flux due to heterogeneities in vegetation cover, among others (Leuning et al. 2012).
In this study, the average value of was 17 (±5.2) s m−1 and 90% of data was <25 s m−1. For , the 88% of the estimated values were <10 s m−1 reaching an average value of 6.2 (±3.4) s m−1. Additionally, 89% of the total observations were <300 s m−1 for and , which presented mean values of 159 (±101) s m−1 and 164 (±104) s m−1, respectively. Estimated values of were between 83 and 418 s m−1, with an average value of 158 (±53) s m−1. Also, the Jarvis-type model subestimated daytime variation of with an error of 1% while RMSE, MBE, and dr were 41 s m−1, 7.0 s m−1, and 0.80, respectively (Table 4).
The validation indicated that the submodel estimated the Rn with values of RMSE = 65 W m−2, MBE = −7.7 W m−2, and dr = 0.99. For the simulation period, the roe value was significantly different from 1.0, suggesting an overestimation of 6%. These results are in accordance to those reported by López-Olivari et al. (2015), who observed that three semiempirical models of Rn presented RMSE values ranging between 26 and 101 W m−2. Major disagreements in the estimation of Rn are usually associated to the effects of cloudy days on the parameterization of , and the use of the uncalibrated Brutsaert’s equation (Ortega-Farias et al. 2010). Additionally, nonrepresentative α values could lead to inadequate estimations of Rn because it is the reflection coefficient for solar radiation (Jones 2013). Thus, using inadequate information may generate under/overestimation of the shortwave radiation available at the surface. On the other hand, the validation for G showed values of RMSE, MBE, and dr equal to 49 W m−2, 1.3 W m−2, and 0.95, respectively. For G, Li et al. (2006) obtained RMSE values ranging between 22 and 25 W m−2 over agricultural landscapes.
Using 30-min time intervals, Table 4 shows that the clumped model estimated the LE with RMSE, MBE, and dr values of 35 W m−2, −1.0 W m−2, and 0.96, respectively. In addition, the roe value was 0.89 and significantly different from the unity, indicating that the clumped model underestimated the LE measured using the EC system by 11%. In the interval 0 < LE < 250 W m−2, the points were close to the 1:1 line (Fig. 2), meanwhile LE values outside this interval exhibited higher scatter. The overall daily comparison between estimated and observed ETa (Table 4) indicated that the clumped model was able to predict the daily water consumption with RMSE, MBE, and dr values of 0.48 mm day−1, 0.04 mm day−1, and 0.64, respectively. Moreover, the roe value was significantly different from 1.0 indicating that ETa was underestimated by 3.0%. Also, Fig. 3 shows that the points were close to 1:1 line for ETa ranging between 1.15 and 4.10 mm day−1. Also, 73% of the absolute differences |LEBR − LEc| were lower than 30 W m−2 (Fig. 4).
The sensitivity analysis of uncertainties in the input parameters is shown in Table 5. For the clumped model, the sensitivity of ETa to uncertainties in C, zo, , , , and dp was small. The greatest variations were between 6.0% and 11.0% for LAI and rstmin, suggesting that the clumped model is sensitive to the parameters controlling the water vapor transfer from canopy to the atmosphere. Thereby, the sensitivity analysis suggested that the accuracy of the clumped model to simulate ETa significantly depended on the measurements of LAI and the used rstmin. In this regard, Villagarcía et al. (2010) indicated that the clumped model was very sensitive to errors in the values of LAI and rst, which are included in the formulation of . Additionally, they also observed important variations of the estimated ETa related to the depth at which the soil water content was measured to the parameterization of and . However, this study was not able to verify the importance of attributed by Were et al. (2008), who evaluated the clumped model over bush–vegetation and semiarid conditions. Additionally, Zhang et al. (2008) found good agreement between the ETa estimated by the clumped model and measurements obtained by the Bowen ratio–energy balance system, but the difference between the observed and estimated values would be mainly affected by and and the inaccurate estimates of energy components in the vegetation and soil. Finally, Poblete-Echeverría and Ortega-Farias (2009) found major disagreements of the clumped model related to the days after rainfall or under foggy conditions (soil surface became wet).
The proper performance of the clumped model could rely on the fact that LAI and water status were almost constant during both seasons as result of the agricultural management. Thus, this research could only be extended to orchards with the same training system, row orientation and irrigation system (drip irrigation) under semiarid climate conditions. First, because the ETa depends on the intercepted solar radiation by the canopy and soil, it may significantly change with variations of interrow width and the hedgerow orientation (Connor et al. 2014; Trentacoste et al. 2015). Second, the estimation of and may be affected by the fraction of wetted soil fw, especially, in the flood and furrow irrigation systems. In this case, submodels using as input fw and soil texture are required to improve the estimation of and . Finally, an appropriate rst estimation is also needed, considering that there are differences of the stomata closure even at the cultivar level. Therefore, the practical application of the clumped model would be limited by a correct description of the canopy architecture and the fractional cover, which takes into account the differences of the intercepted solar radiation by the canopy and the soil.
The clumped model was tested using an EC system installed above a commercial superintensive drip-irrigated olive orchard with a constant value of fc (30%) and LAI (1.32 m2 m−2) during two consecutive growing seasons. The estimation of ETa and LE by the clumped model agreed well with the measurements of the EC system on daily and 30-min periods, respectively. For the two seasons, the clumped model underestimated LE and ETa with errors of 11.0% and 3.0%, respectively. In addition, submodels of Rn, G, and estimated with errors less than 6%. Finally, the sensitivity analysis indicated that the ETa estimated by the clumped model was significantly affected by variations of ±30% in the values of LAI and rst.
These results suggest that it is possible to directly estimate ETa using the clumped model, which was very sensitive to errors in the values of stomatal resistance and leaf area index. Future research will be concentrate on the effect of water stress on the parameterization of Rn, G, and . Also, we will explore the application of the clumped model to flood-irrigated orchards where soil evaporation plays an important role in the water application.
This study was supported by the Chilean government through the projects CONICYT PFCHA/Doctorado Nacional 21141010, CONICYT PAI/Sector Productivo T7816120002, FONDEF (D10I1157), FONDECYT (1100714), and by the University of Talca through the research program “Adaptation of Agriculture to Climate Change (A2C2).” The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.